Decomposition of Anomalous Diffusion in Levy Walks with Finite Step Duration

Diffusive behavior is normally governed by the Central Limit Theorem (CLT), which states that the displacement in the limit of large time has a Gaussian distribution with a width that increases as square root of time. However, diffusive behavior that differs from the CLT is found in a wide array of experimental systems. The root causes of anomalous diffusive behavior can be identified by decomposing the behavior into three fundamental constitutive effects, each of which are associated with the violation of an assumption of the CLT and are known as the Joseph, Noah, and Moses effects. The dynamics of systems with anomalous diffusive behavior are often modeled with generalized Lévy Walks (GLWs) that have steps of random duration chosen from a power law probability distribution and a velocity in each step of magnitude deterministically non-linearly coupled to the duration. The decomposition of anomalous diffusion in GLWs that have an infinite mean step duration was recently completed [E. Aghion et al., New J. Phys. 23 023002 (2021)]. Here, we extend that decomposition to GLWs that have steps of finite mean duration, finding that the anomalous diffusive behavior is generally a complex combination of the three constitutive effects. We further extend the decomposition to analyze variable speed generalized Lévy Walks and show that the Latent exponent L that characterizes the Noah effect has no upper bound.